A Stochastic Model of the 2007 Russian Duma Election

Public Choice (2010) 142: 177–194 DOI 10.1007/s11127-009-9483-2 A stochastic model of the 2007 Russian Duma election Norman Schofield · Alexei Zakharov Received: 11 June 2009 / Accepted: 8 July 2009 / Published online: 24 July 2009 © Springer Science+Business Media, LLC 2009 Abstract In this paper we consider the nature of local Nash equilibrium (LNE) for a model of the 2007 Duma election in Russia, using estimates of valence obtained from sociodemographic variables. We then extend this sociodemographic valence model by including institutional valences, the approval by voters of the various institutions, including the President, the Prime Minister, the State Duma and the Federation Council. We show by simulation that the vote maximizing LNE of this general stochastic model were not at the electoral origin. The dominant feature of the election was the influence of approval or disapproval of President Putin on each voter’s political choice. Keywords Stochastic model · Election · Russian Duma JEL Classification H10 1 Introduction Recent work has argued that institutional characteristics of political systems, such as pres- identialism versus parliamentarianism, or majoritarianism versus proportionality will have significant effects on the size of government and the extent of redistributive politics.1 How- ever, these arguments have been based on cross country empirical analyses, sometimes com- bined with a relatively simple one dimensional spatial model (Downs 1957; Riker and Or- 1Bawn and Rosenbluth (2005) and Persson and Tabellini (2000, 2003). N. Schofield () Center in Political Economy, Washington University in Saint Louis, Saint Louis, USA e-mail: schofi[email protected] A. Zakharov Department of Higher Mathematics at the Economics Faculty, Higher School of Economics, 101000 Moscow, Russia e-mail: [email protected] 178 Public Choice (2010) 142: 177–194 deshook 1973) which emphasizes the location of the median voter. The present paper fo- cuses on constructing an empirical model of the election in Russia in 2007, involving a large number of parties, in a situation where the policy space can be assumed to consist of two or more dimensions. We use a formal apparatus that has already proved useful in account- ing for party position in a variety of countries, including Israel, the Netherlands, the United Kingdom and the United States.2 The formal model which we use is based on the assumption that elections are partly based on the judgments of voters as regards the competence or quality of party leaders or political candidates. In this respect, the formal model can be linked to Madison’s under- standing of the nature of the choice for the president of the United States. Schofield (2006a) has suggested that Madison’s argument may well have been influenced by Condorcet’s work on the so-called “Jury Theorem” (Condorcet 1785). Condorcet’s work has recently received renewed attention (Ladha 1992, 1993; McLennan 1998) and formal models have been presented based on the notion of valence, the perception of the quality of the political leader (Ansolabehere and Snyder 2000; Groseclose 2001; Aragones and Palfrey 2002, 2005;Za- kharov 2009). The work in this research program can be seen as a contribution to the devel- opment of a Madisonian conception of elections in representative democracies as methods of aggregation of both preferences and judgments (Madison 1787). The usual spatial model is based on the assumption that it is only candidate positions that matter to voters. However, as Stokes (1963, 1992) has emphasized many years ago, the non-policy evaluations, or valences, of candidates by the electorate are equally important. Recent empirical work by Clarke et al. (2009a: 159) has compared a ‘Downsian’ or spatial model of the 2000 US presidential election with a valence model of the same election, based on the perceptions of the character traits of the candidates by the voters. They found that “the two models have equal explanatory power.” This paper develops a stochastic electoral model which combines elements of the Down- sian stochastic vote model with ‘Stokesian’ valence, in which each candidate or party leader is characterized by an intrinsic valence (or quality). The estimates of intrinsic valence for each party were obtained as intercept terms from a standard multinomial conditional logit (MNL) model of the election. The underlying policy space was obtained from factor analy- sis of positive/negative responses to a list of forty concepts, such as ‘Capitalism’ and ‘the Church’, etc. We then examined the conditions for existence of ‘a local Nash equilibrium’ (LNE) under vote maximization. A LNE is simply a vector of party positions with the property that no party may make a small unilateral move and yet increase utility (or vote share). Schofield (2007) has presented a theorem which gives the necessary and sufficient conditions for the validity of the mean voter theorem, that all parties should converge to the electoral origin.3 This result is presented in terms of a ‘convergence coefficient’ incorporating all the parameters of the model. This coefficient, c, involves the differences in the exogenous valences of the party leaders, and the ‘spatial coefficient’, β. When the policy space, X, is assumed to be of dimension w, then the necessary condition for existence of an LNE when all parties are located at the electoral origin is that the coefficient c is bounded above by w.When the necessary condition fails, then parties, in equilibrium, will adopt divergent positions. In 2See Miller and Schofield (2003, 2008), Schofield et al. (2003), Schofield and Miller (2007), Schofield and Sened (2005, 2006). 3The electoral origin is the mean of the distribution of voter preferred points. A vector of party positions when all parties are at the origin is termed the joint origin. Public Choice (2010) 142: 177–194 179 general, parties whose leaders have the lower valences will take up positions further from the electoral mean. Simulation of a four-party model for the 2007 Russian Duma election showed that the condition for convergence was satisfied. Indeed, simulation of the model did indicate that the joint origin was a LNE. We then incorporated sociodemographic characteristics in what we call the joint model. These sociodemographic variables included ‘education’, ‘income’, ‘age’, ‘gender’. Such variables are used frequently to estimate the propensity of different subgroups in the polity to choose one party over another. They can be regarded as sociodemographic valences, generated by common perceptions of the parties by different societal subgroups. We also incorporated a number of variables related to the perception of the voter as to the nature or quality of government institutions, including ‘general efficacy’ (whether the voter had a say in policies), ‘approval of the president’, ‘approval of the prime minister’, ‘approval of the State Duma’, and ‘approval of the Federation Council’. The ‘approval of President Putin’ had a significant and negative effect on the support for two of the parties, the Liberal Democratic Party of Russia (LDPR) and Fair Russia (SR). Because these perceptions are tied to individuals who are located in the policy space, the LNE positions, in principle, will depend on how these perceptions are distributed among the electorate. We developed a simulation package based on a gradient technique which allowed us to estimate vote maximizing LNE of any such spatial model. The position of each party in the LNE of this model was termed the weighted electoral mean of the party. To account for the difference between the vector of weighted electoral means and the estimated vector of party positions, we introduced the notion of activist valences. In this more general model, activists are assumed to provide political and economic resources to parties, who then use these resources to enhance their image before the electorate.4 We suggest that the influence of activists was relatively insignificant in this election, with electoral perception of Putin the most important component of the election. The next section presents the formal model, followed by the empirical model and some concluding remarks. 2 A stochastic model of elections Details of the pure spatial stochastic electoral model are given in Schofield (2007). This model is an extension of the standard multiparty stochastic model, modified by inducing asymmetries in terms of valence. The model is denoted M(λ,β), where voter utility is given by the expression 2 uij (xi ,zj ) = λj − βxi − zj + εj . (1) Here the intrinsic valence vector λ = (λ1,λ2,...,λp) satisfies λp ≥ λp−1 ≥···≥λ2 ≥ λ1, where (1,...,p) label the parties, and λj is the intrinsic valence of party j. In empirical models, the valence vector λ is given by the intercept terms. The points {xi: i ∈ N} are the preferred policies of the voters and {zj : j ∈ P } are the positions of the parties. The term xi − zj is simply the Euclidean distance between xi and zj . The error vector (ε1,...,εp) is distributed by the type I extreme value distribution, . 4This feature of the model was based on earlier work by Aldrich (1983). 180 Public Choice (2010) 142: 177–194 We can also define a stochastic electoral model, which utilizes socio-demographic variables and voter perceptions of institutional quality. For this model we assume that voter i utility is given by the expression 2 uij (xi ,zj ) = λj + (θj · ηi ) + (αj · τi ) − βxi − zj + εj . (2) Here θ is a set of k-vectors {θj : j ∈ P } representing the effect of the k different sociodemographic parameters (age, education, income, gender, rural/urban, religious orientation) on voting for party j while ηi is a k-vector denoting the ith individual’s relevant “sociodemographic” characteristics. The compositions {(θj · ηi )} are scalar products, called the sociodemographic valences for j. Similarly, the terms {(αj · τij )} are scalar products, giving voter i’s perception of the quality of various political institutions, such as the President, Prime Minister, the State Duma and the Federation Council.

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